A skewed truncated Cauchy uniform distribution and its moments
Although usually normal distribution is considered for statistical analysis, however in many practical situations, distribution of data is asymmetric and using the normal distribution is not appropriate for modeling the data. Base on this fact, skew symmetric distributions have been introduced. In t...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Canadian Center of Science and Education
2016
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| Online Access: | http://psasir.upm.edu.my/id/eprint/54940/1/A%20Skewed%20Truncated%20Cauchy%20Uniform%20Distribution%20and%20Its%20Moments.pdf |
| _version_ | 1796976174410235904 |
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| author | Ashani, Zahra Nazemi Abu Bakar, Mohd Rizam Ibrahim, Noor Akma Adam, Mohd Bakri |
| author_facet | Ashani, Zahra Nazemi Abu Bakar, Mohd Rizam Ibrahim, Noor Akma Adam, Mohd Bakri |
| author_sort | Ashani, Zahra Nazemi |
| collection | UPM |
| description | Although usually normal distribution is considered for statistical analysis, however in many practical situations, distribution of data is asymmetric and using the normal distribution is not appropriate for modeling the data. Base on this fact, skew symmetric distributions have been introduced. In this article, between skew distributions, we consider the skew Cauchy symmetric distributions because this family of distributions doesn't have finite moments of all orders. We focus on skew Cauchy uniform distribution and generate the skew probability distribution function of the form , where is truncated Cauchy distribution and is the distribution function of uniform distribution. The finite moments of all orders and distribution function for this new density function are provided. At the end, we illustrate this model using exchange rate data and show, according to the maximum likelihood method, this model is a better model than skew Cauchy distribution. Also the range of skewness and kurtosis for and the graphical illustrations are provided. |
| first_indexed | 2024-03-06T09:22:01Z |
| format | Article |
| id | upm.eprints-54940 |
| institution | Universiti Putra Malaysia |
| language | English |
| last_indexed | 2024-03-06T09:22:01Z |
| publishDate | 2016 |
| publisher | Canadian Center of Science and Education |
| record_format | dspace |
| spelling | upm.eprints-549402018-06-12T08:20:29Z http://psasir.upm.edu.my/id/eprint/54940/ A skewed truncated Cauchy uniform distribution and its moments Ashani, Zahra Nazemi Abu Bakar, Mohd Rizam Ibrahim, Noor Akma Adam, Mohd Bakri Although usually normal distribution is considered for statistical analysis, however in many practical situations, distribution of data is asymmetric and using the normal distribution is not appropriate for modeling the data. Base on this fact, skew symmetric distributions have been introduced. In this article, between skew distributions, we consider the skew Cauchy symmetric distributions because this family of distributions doesn't have finite moments of all orders. We focus on skew Cauchy uniform distribution and generate the skew probability distribution function of the form , where is truncated Cauchy distribution and is the distribution function of uniform distribution. The finite moments of all orders and distribution function for this new density function are provided. At the end, we illustrate this model using exchange rate data and show, according to the maximum likelihood method, this model is a better model than skew Cauchy distribution. Also the range of skewness and kurtosis for and the graphical illustrations are provided. Canadian Center of Science and Education 2016 Article PeerReviewed text en http://psasir.upm.edu.my/id/eprint/54940/1/A%20Skewed%20Truncated%20Cauchy%20Uniform%20Distribution%20and%20Its%20Moments.pdf Ashani, Zahra Nazemi and Abu Bakar, Mohd Rizam and Ibrahim, Noor Akma and Adam, Mohd Bakri (2016) A skewed truncated Cauchy uniform distribution and its moments. Modern Applied Science, 10 (7). 174 - 182. ISSN 1913-1844; ESSN: 1913-1852 10.5539/mas.v10n7p174 |
| spellingShingle | Ashani, Zahra Nazemi Abu Bakar, Mohd Rizam Ibrahim, Noor Akma Adam, Mohd Bakri A skewed truncated Cauchy uniform distribution and its moments |
| title | A skewed truncated Cauchy uniform distribution and its moments |
| title_full | A skewed truncated Cauchy uniform distribution and its moments |
| title_fullStr | A skewed truncated Cauchy uniform distribution and its moments |
| title_full_unstemmed | A skewed truncated Cauchy uniform distribution and its moments |
| title_short | A skewed truncated Cauchy uniform distribution and its moments |
| title_sort | skewed truncated cauchy uniform distribution and its moments |
| url | http://psasir.upm.edu.my/id/eprint/54940/1/A%20Skewed%20Truncated%20Cauchy%20Uniform%20Distribution%20and%20Its%20Moments.pdf |
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